I'd recommend the phone that I have, the Oneplus Two. I have the 64GB version and it has been flawless so far, its going to cost me less than half of what the S6 Edge I was looking at was going to cost. The battery last a couple days, the camera can record in 4K and 120FPS slow motion. It also has completely stock android with no annoying apps than come standard on Samsung and stuff. The phone only cost me £250 and I got a contract sim on deal for £5.50 a month. Although the Oneplus X is a really nice looking phone so you may also want to look at that, it is also slightly cheaper. The S6 Edge is another good phone I'd recommend but I don't feel its worth the extra money over the OP2 after trying both, the feel the same speed.

I'd recommend the LG G4. I currently have this phone and it's totally amazing! The picture quality is insane, espically for close up shots, considering its for a phone camera.

Oneplus two was my second option before I bought the LG G4. The only drawback that my friend, and many other people have noticed, is that the phone can heat up a lot (caused by the snap dragon 810 processor). But looking at the price, it's deffo a flagship killer!

I own a Nokia Lumia 1020 which I highly recommend (even though you said you're not a fan of Windows phones). Great camera (1080p), does everything a smartphone should and 32/64GB but I have a 32GB SD card in there as well, mostly for my music.